Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
import sys
import os
from math import*
input=sys.stdin.buffer.readline

n=int(input())
x=int(max(int((-1+sqrt(1+8*n))//2),(-1-sqrt(1+8*n))//2))
z=0
while x>0:
	c=n-(x*(x+1)//2)
	if c==0:
		x-=1
	else:
		k=int(max(int((-1+sqrt(1+8*c))//2),(-1-sqrt(1+8*c))//2))
		if k*(k+1)//2==c:
			z=1
			break
		else:
			x-=1
if z==1:
	print("YES")
else:
	print("NO")